Advanced Analysis of Variance

Books

Introducing a revolutionary new model for the statistical analysis of experimental data

In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data. Dr. Hirotsu introduces the groundbreaking concept of advanced analysis of variance (AANOVA) and explains how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions.

Focusing on normal, binomial, and categorical data, Dr. Hirotsu explores ANOVA theory and practice and reviews current developments in the field. He then introduces three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from categorical data. Using real-world examples, he shows how these three recognizable families of problems have important applications in most practical activities involving experimental data in an array of research areas, including bioequivalence, clinical trials, industrial experiments, pharmaco-statistics, and quality control, to name just a few.

• Written in an expository style which will encourage readers to explore applications for AANOVA techniques in their own research

Introducing a breakthrough approach to statistical analysis which overcomes the limitations of the ANOVA model, Advanced Analysis of Variance is an indispensable resource for researchers and practitioners working in fields within which the statistical analysis of experimental data is a crucial research component.

Chihiro Hirotsu is a Senior Researcher at the Collaborative Research Center, Meisei University, and Professor Emeritus at the University of Tokyo. He is a fellow of the American Statistical Association, an elected member of the International Statistical Institute, and he has been awarded the Japan Statistical Society Prize (2005) and the Ouchi Prize (2006). His work has been published in Biometrika, Biometrics, and Computational Statistics & Data Analysis, among other premier research journals.

Preface xi

Notation and Abbreviations xvii

1 Introduction to Design and Analysis of Experiments 1

1.1 Why Simultaneous Experiments? 1

1.2 Interaction Effects 2

1.3 Choice of Factors and Their Levels 4

1.4 Classification of Factors 5

1.5 Fixed or Random Effects Model? 5

1.6 Fisher’s Three Principles of Experiments vs. Noise Factor 6

1.7 Generalized Interaction 7

1.8 Immanent Problems in the Analysis of Interaction Effects 7

1.9 Classification of Factors in the Analysis of Interaction Effects 8

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